show that the following determinant vanishes:

| a-b b-c c-a b-c c-a a-b c-a a-b b-c|

A=a-bb-cc-ab-cc-aa-bc-aa-bb-cNow using R1R1+R2+R3A=a-b+b-c+c-ab-c+c-a+a-bc-a+a-b+b-cb-cc-aa-bc-aa-bb-c=000b-cc-aa-bc-aa-bb-c=0 As row 1 is 0

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